1. Field of the Invention
The present invention relates to the field of optically pumped atomic clocks or magnetometers, and more particularly to atomic clocks or magnetometers that operate by probing 0-0 coherent population trapping (CPT) resonances using light of alternating polarization referred to as push-pull pumping.
2. Description of the Related Art
Conventional, gas-cell atomic clocks utilize optically pumped alkali-metal vapors. Atomic clocks are utilized in various systems that require extremely accurate frequency measurements. For example, atomic clocks are used in GPS (global positioning system) satellites and other navigation and positioning systems, as well as in cellular phone systems, radio communications, scientific experiments and military applications. A design similar to that of an atomic clock is also utilized as a magnetometer, since some of the atomic resonances are highly sensitive to the magnetic field.
In one type of atomic clock, a cell containing an active medium, such as rubidium or cesium vapor, is irradiated with both optical and microwave power. The cell contains a few droplets of alkali metal and an inert buffer gas (such as N2, any of the noble gases, or a mixture thereof) at a fraction of an atmosphere of pressure. Light from the optical source pumps the atoms of the alkali-metal vapor from a ground state to an optically excited state, from which the atoms fall back to the ground state, either by emission of fluorescent light or by quenching collisions with a buffer gas molecule such as N2. The wavelength and polarization of the light are chosen to ensure that some ground state sublevels are selectively depopulated, and other sublevels are overpopulated compared to the normal, nearly uniform distribution of atoms between the sublevels. The resonant transitions (or resonances) between these sublevels can be probed by the microwaves. It is also possible to excite the same resonances by modulating the light at the Bohr frequency of the resonance (a method currently known as coherent population trapping, or CPT), as first pointed out by Bell and Bloom, W. E. Bell, and A. L. Bloom, Phys. Rev. Lett. 6, 280 (1961), hereby incorporated by reference into this application. The changes in the ground state of alkali-metal atoms, introduced by the resonance, lead to a change in the transparency of the vapor, so a different amount of light passes through the vapor to a photo detector that measures the transmission of the pumping beam, or to photo detectors that measure fluorescent light scattered out of the beam. When an applied magnetic field, produced by the microwaves, oscillates with a frequency equal to one of the Bohr frequencies of the atoms, the populations of the ground-state sublevels are perturbed and the transparency of the vapor changes. If excitation by the modulated light (CPT) is used instead of the microwaves, a coherent superposition state of the ground-state sublevels is generated when the light modulation frequency or one of its harmonics matches one of the Bohr frequencies of the atoms. The changes in the transparency of the vapor are used to lock a clock or a magnetometer to the Bohr frequencies of the alkali-metal atoms.
The Bohr frequencies of a gas-cell atomic clock are the frequencies v with which the electron spin S and the nuclear spin I of an alkali-metal atom precess about each other and about an external magnetic field. For the ground state, the precession is caused by magnetic interactions. Approximate clock frequencies are v=6.835 GHz for 87Rb and v=9.193 GHz for 133Cs. Conventionally, clocks have used the “0-0” resonance which is the transition between an upper energy level with azimuthal quantum number m=0 and total angular momentum quantum number F=I+½, and a lower energy level, also with azimuthal quantum number m=0 but with total angular momentum quantum number F=I−½.
Conventionally, to excite CPT resonances, frequency-modulated (FM) or phase-modulated (PM) optical-pumping light with wavelengths close to the D1 or D2 resonance lines of the atom (shown in FIG. 1A) are used. The light is modulated at a microwave frequency v close to one half of the 0-0 resonance frequency v0, shown in FIG. 1B. The modulation amplitude and the carrier frequencies are chosen to optimize the sideband spectrum for CPT signals. The time-averaged transparency of the vapor increases when v=v0/2. The full width at half maximum of this CPT resonance can be less than 1 kHz. The amplitude of the 0-0 CPT resonance is not very large, often amounting to an increase in the time-averaged transmission by less than 1%. The frequency v0 of the 0-0 resonance has a very weak, quadratic dependence on the magnetic field, so some control of the magnetic field is needed to stabilize the clock.
In FIG. 1A, the atomic energy levels and the optical transitions are shown for an optically pumped atomic clock. The ground state of an alkali-metal atom, illustrated with 87Rb, is split into hyperfine sublevels by the Fermi contact interaction between the electronic spin, with quantum number S=1/2, and the nuclear spin, with quantum number I=3/2. An expanded diagram of the ground-state sublevels of 87Rb is shown in FIG. 1B. The hyperfine splitting separates the energies of sublevels with the total angular momentum quantum number F=I+S=2 from those with F=I−S=1. The energies of sublevels with the same F but different azimuthal quantum numbers m are shifted relative to each other by the magnetic field. Pumping alkali-metal atoms with D1 resonance light of fixed circular polarization drives the ground-state population distribution toward the end states of maximum or minimum m, depending on the sense (right or left) of circular polarization of the light. For high-density vapor, where spin-exchange collisions are the dominant spin-relaxation mechanism, or at high buffer-gas pressures, a spin-temperature population distribution similar to the one illustrated by the vertical bars in FIG. 1B is produced. For lower buffer-gas pressures and slower spin-exchange rates, the distributions are qualitatively similar, but differ in detail. The build up of the population in the end states results in very large microwave and Zeeman end resonance signals at frequencies vm and vz, as illustrated in FIG. 1B. However, the 0-0 resonance signal at v0 is very small, since the build up of population in the end state leaves few atoms in the initial and final states of the 0-0 resonance.
It has been found that the 0-0 resonance excited and probed by frequency-modulated light becomes too small for practical use at buffer-gas pressures exceeding a few hundred torr as described in D. E. Nikonov et al., Quantum Opt. 6, 245 (1994). Broadening of the optical absorption lines degrades the CPT signals generated with frequency modulated light in much the same way, and for analogous reasons, as decreasing the Qs (quality factors) of the two tuned circuits degrades the performance of phase-shift discriminators of FM radio or television receivers. The population concentration in the end state and the suppression of the 0-0 resonance also occurs when the pumping is done with unmodulated light of fixed circular polarization, and it is independent of whether the resonances are excited by microwaves, or with the circularly polarized light that is frequency-modulated at v0/2, half the 0-0 frequency.
Conventional CPT atomic clock systems have used modulated light of fixed polarization. It has been found that less degradation of the 0-0 CPT resonances with increasing buffer gas pressure occurs if light of fixed circular polarization is intensity-modulated at the frequency v0 instead of being frequency-modulated at v0/2.
Modeling calculations of population distributions and CPT resonances produced by intensity-modulated, right-circularly-polarized (RCP) light are shown in FIGS. 2A–C for 87Rb. The intensity-modulation pattern of RCP D1 pumping light is shown in FIG. 2A. The atomic population distribution among the ground-state sublevels is shown in FIG. 2B. The circularly polarized light pumps the atoms toward the end state of maximum azimuthal spin quantum number m, and away from the m=0 states participating in the resonance. FIG. 2C shows the calculated CPT resonance in the time-averaged absorption cross-section {overscore (σ)} of the atoms, normalized to the cross section σ0 for unpolarized atoms. The detuning ω-ω0 of the modulation frequency ω from the resonance frequency, ω0=2πv0, is normalized to the S-damping rate Γsd. Buffer gas pressures are assumed which are high enough to seriously degrade the FM or PM CPT. It is shown that the CPT resonance with intensity modulated light is barely visible, as a small decrease in the time-averaged cross section {overscore (σ)}, which is plotted in units of the absorption cross section σ0 of completely unpolarized atoms. For the modeling calculations of FIGS. 2A–C, a mean optical pumping rate Γop was used which was three times the S-damping rate Γsd of spins in the gas, i.e. Γop=3 Γsd. It was assumed that a small additional spin loss occurs at a rate Γ=0.01Γsd due to diffusion of alkali-metal atoms to the walls. The instantaneous pumping rate of the RCP light was assumed to have the time dependence R=Γop(2Pp!)2[2(2p)!]−1 cos2p πv0t with p=2. Any intensity modulation format with a similar time dependence gives comparable results.
The CPT signal with pulsed light of fixed circular-polarization at very high buffer-gas pressure has about the same amplitude as the CPT signal at low pressures with frequency-modulated light. In both cases, the small signal amplitude is due to the accumulation of most of the atoms in the end state, as shown in FIG. 2B. The suppression of the 0-0 CPT signal due to optical pumping has been discussed in J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, Phys. Rev. A 67, 065801 (2003).
It is desirable to provide a method and system to increase the intensity of 0-0 coherent popularity trapping (CPT) resonances in alkaline-metal vapors.